Is the word sorvete the same in Brazilian and European Portuguese?

No

The difference between the two lies in typical usage. While the word "sorvete" is understood in Portugal, it is not the natural or standard term used in daily conversation. In Portugal, the standard word for ice cream is gelado. Additionally, there is a difference in pronunciation: in Brazil, the final "e" is typically pronounced as a soft "i" (sor-vê-ti), whereas in Portugal, the vowel sounds are generally more closed and the syllable stress follows European phonetic patterns.

Brazilian Portuguese Usage

1. Eu adoro comer sorvete quando está calor. (I love eating ice cream when it's hot.)
2. Você prefere sorvete de baunilha ou de chocolate? (Do you prefer vanilla or chocolate ice cream?)
3. O sorvete derreteu muito rápido no sol. (The ice cream melted very quickly in the sun.)
4. Vamos passar na sorveteria depois do almoço? (Shall we stop by the ice cream parlor after lunch?)
5. Comprei um pote de sorvete para a sobremesa. (I bought a tub of ice cream for dessert.)

Continental Portuguese Usage

1. Eu adoro comer gelado quando está calor. (I love eating ice cream when it's hot.)
2. Preferes gelado de baunilha ou de chocolate? (Do you prefer vanilla or chocolate ice cream?)
3. O gelado derreteu muito rápido ao sol. (The ice cream melted very quickly in the sun.)
4. Vamos passar na gelataria depois do almoço? (Shall we stop by the ice cream parlor after lunch?)
5. Comprei um pote de gelado para a sobremesa. (I bought a tub of ice cream for dessert.)